The mechanical properties of non-vulcanized natural rubber and dialyzed natural rubber-clay nanocomposites have been studied by uniaxial deformations to evaluate the reinforcement efficiency of the clay. We show that while non-rubber molecules contribute to auto-reinforcement, removal of these molecules improves significantly the performance of clay as reinforcement agent. These mechanical properties are discussed in relation to morphological aspects of the clay characterized by TEM and SANS. The nanocomposites prepared by "latex-mixing" with aqueous dispersions of clay are found to contain completely exfoliated clay lamellae in coexistence with tactoids. Improved mechanical properties of the nanocomposites can be modeled by the high aspect ratio of exfoliated clay platelets coupled with immobilized rubber matrix. Interestingly, presence of tactoids does not appear to compromise the excellent reinforcement properties of the exfoliated platelets. At high deformations, strain-induced alignment of the clay exhibits anisotropic scattering, with anisotropy increasing with clay concentration and stretching.